Homework SourseIt is known that x 1 x is an integer number Show that xn 1x
It is known that x+ 1/ x is an integer number. Show that x*n + 1/x*n is also an integer number for any natural n.
Solution
=>(xn-1+1/xn-1)(x+1/x)=xn+1/xn-2+xn-2+1/xn=(xn+1/xn)+(xn-2+1/xn-2)
xn+1/xn=(xn-1+1/xn-1)(x+1/x)-(xn-1+1/xn-2)
where is an integer so the induction gets
